I have finally received my TTL cable, and can now view the Bootlog for my Sama5d3 Xplained.
What I have done:
1) Ran the demo retrieved from ftp://ftp.linux4sam.org/pub/demo/linux4sam_5.8/
by placing the files in the same directory as sam-ba and then executing the command "./demo_linux_nandflash.sh" which is successful and the board boots normally.
2) I built and Image and dtbs for the board by doing the following:
cd linux-at91
export CROSS_COMPILE=arm-linux-gnueabi-
export ARCH=arm
make sama5_defconfig
make

The resulting binaries used are: ~/linux-at91/arch/arm/boot/zImage
and ~/linux-at91/arch/arm/boot/dts/at91-sama5d3_xplained.dtb

Then I went back to the sam-ba directory, where I ran the command:
./sam-ba -p serial -b sama5d3-xplained -a nandflash -c erase:0x180000:0x400000 -c write:at91-sama5d3_xplained.dtb:0x180000 -c write:zImage:0x200000

Upon download of these two binaries, I then hit the Reset button (BP2) and the following Bootlog is the output:
AT91Bootstrap 3.8.10 (Wed Mar 28 19:46:50 CEST 2018)

Actually you have not, but there is just enough information that indicates two possible sources that could cause a boot failure.
However your title is bogus, and does not reflect the problem you are encountering.
Where is this "RomBoot" [sic] in your boot log?
There's clearly a data abort exception that is reported in the log, yet you ignore that and call it "Freezing at "Resetting CPU""?
The first salient step in problem solving is to properly describe and identify the problem.

(You need to learn how to use the quote and code tags to properly format your post.)
This is the first point where boot failure could have been induced.
You only specified that NAND flash should be erased for 0x400000 bytes starting at offset 0x180000.
Assuming that aligns with an erase block, that erase operation only allocates NAND area 0x00200000 to 0x580000 for the kernel image.
If your zImage file is larger than 0x380000 bytes, then the complete image may not be properly stored in NAND.

Bader97 wrote: ↑
Upon download of these two binaries, I then hit the Reset button (BP2) and the following Bootlog is the output:
AT91Bootstrap 3.8.10 (Wed Mar 28 19:46:50 CEST 2018)
...
U-Boot 2017.03-linux4sam_5.8 (Mar 28 2018 - 19:46:54 +0200)

A report of the U-Boot environment would be ideal, since that is the second point where boot failure can be induced.
So I'll assume that you're blindly using the existing U-Boot environment of Linux4SAM_5.8, which has :

This bootcmd has a nasty customization of specifying the exact sizes of the .dtb and zImage files read from the NAND flash into memory.
If your replacement files that you built are larger than the demo files, then this bootcmd will not properly load them.

A data abort exception is the likely outcome of trying to execute a truncated zImage.
Of course there are other possible causes for a data abort, but these two obvious issues need to be resolved first.

Thank you for your reply, and I apologize for my sloppiness but I am not too experienced with community discussions. Your U-boot Environment comment is remarkable; it helped me understand a lot more about how this board works.

Since then, I have reboot the board, stopped the autoboot (by pressing any button), changed the U-boot Environment by doing
"editenv bootcmd" and then changed
this: "bootcmd=nand read 0x21000000 0x00180000 0x87c2; nand read 0x22000000 0x00200000 0x375ea0; bootz 0x22000000 - 0x21000000"
to this: "bootcmd=nand read 0x21000000 0x00180000 0x87c2; nand read 0x22000000 0x00200000 0x3b9fe0; bootz 0x22000000 - 0x21000000" since the size of the zImage I am using is 3,907,552 bytes.
after that I used "saveenv" to save these settings and then i did a "boot" command.

One thing I noticed is that I cannot seem to change the first line of the "bootcmd" environment. I am not sure why that is, so I did not change the .dtb file and only changed the kernel image.

Nevertheless, the bootloader did not abort, and using the command "uname -a" gave me the updated kernel image time, which is exactly what I've been trying to achieve.

Again I would like to thank you for your help, and to apologize for my formatting.